The turning of couple - class-XII

A couple when applied to a body it produce 

Consider the point at which resultant of the forces will act, is 'x' m from the point A.

Thus the point is (1.5 - x) m far from the point B.

Thus, using the formula Torque = Distance x Force acting

$20x = 30(1.5 - x)$

or,$ 2x = 4.5 - 3x$

or,$ 5x = 4.5$

or, $x = 0.9m or 90cm$

Thus the resultant point will be 0.9 m or 90 cm far from point A

For the seesaw to balance, the torques must be equal: 10kg * x = 15kg * (2.5m - x). Solving this gives 10x = 37.5 - 15x, so 25x = 37.5, which means x = 1.5m from the center. None of the options match exactly, but 1.7m is the closest provided.

A couple consists of two parallel forces that are equal in magnitude, opposite in sense and do not share a line of action. It does not produce any translation, but only rotational motion.

A couple consists of two equal and opposite forces whose lines of action are parallel and laterally separated by the some distance. Therefore, net force (or resultant) of a couple is null vector, hence there is no translational acceleration, only rotational motion will be there.

True , because a couple donot  produces any linear acceleration it only produces only rotation but single force will produce linear acceleration too.

A couple consists of two equal and opposite parallel forces whose lines of action do not coincide, resulting in pure rotation about the center of mass.

A couple consists of two equal and opposite forces acting at a separation, so that net force becomes zero. When a couple acts on a body it rotates the body but does not produce any translatory motion. Hence, only rotational motion is produced.

A couple has to be applied to the tap in order to open it. A couple is the combination of two equal and opposite parallel forces acting at different axes. Thus option D is correct.

$\left[ MOI \right] =\left[ M{ R }^{ 2 } \right] =\left[ { M }^{ 1 }{ L }^{ 2 }{ T }^{ 0 } \right] \ \left[ Pressure \right] =\left[ N/{ M }^{ 2 } \right] =\left[ { M }^{ 1 }{ L }^{ -1 }{ T }^{ -2 } \right] \ \left[ Couple \right] =\left[ N.{ M } \right] =\left[ { M }^{ 1 }{ L }^{ 2 }{ T }^{ -2 } \right] $

$Power\quad P=100kW\quad =100000W\ w=1800\times \cfrac { 2\pi  }{ 60 } \quad rad/s\ \quad =60\pi \quad rad/s\ P=torque\times w\ torque=530.5\quad Nm$